Abstract: This paper is devoted to the extension of the recently proposed conditionalsymmetry method to first order nonhomogeneous quasilinear systems which areequivalent to homogeneous systems through a locally invertible pointtransformation. We perform a systematic analysis of the rank-1 and rank-2solutions admitted by the shallow water wave equations in 2 + 1 dimensionsand construct the corresponding solutions of the rotating shallow water waveequations. These solutions involve in general arbitrary functions depending onRiemann invariants, which allow us to construct new interesting classes ofsolutions.